Social relationships such as friendship and partner choice are ruled by the proximity principle, which states that the more similar two individuals are, the more likely they will become friends. However, proximity, similarity, and friendship are concepts with blurred edges and imprecise grades of membership. This study shows how to simulate these friendship dynamics in an agent-based model that applies fuzzy sets theory to implement agent attributes, rules, and social relationships, explaining the process in detail. Although in principle it may be thought that the use of fuzzy sets theory makes agent-based modelling more elaborated, in practice it saves the modeller from taking some arbitrary decisions on how to use crisp values for representing properties that are inherently fuzzy. The consequences of applying fuzzy sets and operations to define a fuzzy friendship relationship are compared with a simpler implementation, with crisp values. By integrating agent computational models and fuzzy set theory, this paper provides useful insights into scholars and practitioners to tackle the uncertainty inherent to social relationships in a systematic way.